This question answers why Linux can't run OSX apps, but is there some application similar to Wine that allows one to do so?
Since wine is a re-implementation of the Windows API - you're looking for a re-implementation of the Macintosh API or various "kits" that Apple provides to let OSX apps link to the system frameworks. I don't know of any that fit the bill. The only thing even close is the Chamelion Project which brings the UIKit from iOS to Mac OS X.
Since I don't have a real library for you, Lion is allowed to be virtualized on Mac hardware. Perhaps that would work for your needs while you wait for a lighter implementation like wine?
There are about a hundred hits on Google about "how to run lion in vmware" and all basically point to the check for a server plist file presence check that the installer wants to see before it will proceed. Here is one that's fairly clear on the steps.
The Darling Project was started a short while ago and, while it is far from ready, is probably what you are looking for. It is a Wine-like compatibility layer for running OS X applications on Linux, and looks pretty promising.
There's not a complete one.
Bear in mind that Mac OS X started life as NeXTSTEP, of which OpenStep is a compatible implementation. Or rather, was at one time, so the story goes. Since then at Apple the NextStep frameworks have evolved into Cocoa. Cocoa has over 10 years of additions, extensions and improvements that don't exist in OpenStep.
From what I understand (and this is only hearsay and probably not verifiable outside of Apple) some of the applications included in the Developer Preview of OS X (pre 10.0) would have been able to run on Linux (or Solaris or Windows for that matter) with OpenStep if you were able to get your hands on the source code and compile it. Some of the OpenStep applications (e.g., File Manager/Finder, Mail, Dock, Preview, et al.) look and function strikingly similar to the versions shipping in OS X 10.0, but with the Aqua skin.